Unique ergodicity of free shifts and some other automorphisms of C*-algebras
Abstract
Description
A notion of unique ergodicity relative to the fixed-point subalgebra is defined for automorphisms of unital C*-algebras. It is proved that the free shift on any reduced amalgamated free product C*-algebra is uniquely ergodic relative to its fixed-point subalgebra, as are autormorphisms of reduced group C*-algebras arising from certain automorphisms of groups. A generalization of Haagerup's inequality, yielding bounds on the norms of certain elements in reduced amalgamated free product C*-algebras, is proved.
The revision (2006/08/16) includes a comment that our generalization of Haagerup's inequality can, in fact, be obtained from Ricard+Xu's results, and some other minor changes
The revision (2006/08/16) includes a comment that our generalization of Haagerup's inequality can, in fact, be obtained from Ricard+Xu's results, and some other minor changes